What we learned about the Proton from HERA

Christoph Grab, ETH Zürich, CH-8093 Zürich


1 Introduction

One of the main physics goals of the experiments H1 and ZEUS, operating at the HERA (“Hadron Electron Ring Anlage”) collider at DESY (Hamburg) was the detailed investigation of the proton substructure up to the highest attainable energies [1]. HERA follows the tradition of the “Rutherford Scattering Experiments” and uses pointlike leptons to probe the substructure of the composite object proton. Unlike in earlier fixed target experiments, colliding beams (electrons1 at 27.6 GeV and protons up to 920 GeV) produced centre-of-mass energies up to 319 GeV, extending the available kinematic regions by orders of magnitude. After successful operation for over a decade (1992 - 2007), the HERA collider was finally shut down on 1.7.2007.

The experiments have produced a wealth of results of highest scientific interest. Besides studies of the proton structure as described herein, detailed investigations of the theory of strong interactions (Quantum Chromodynamics QCD), heavy quark physics, searches for phenomena beyond the standard model and many others have been performed (see [1]). Analyses of the accumulated data still continues, and further results will continue to emerge in the future. Not only will these results become an integral part of future physics text books, but they also are of imminent relevance for the physics studies at the “Large Hadron Collider” (LHC) at CERN.

1 HERA operated with both lepton charges, however in the following the generic name “electron” is used to denote both electron and positron.

Figure 1a: Schematic representations of electron proton scattering processes, as viewed in the quark parton model (see text), where the incoming pointlike e scatters on one of the constituents of the composite proton. Neutral current processes ep → e'X (top) are mediated by photons or Z-bosons, and charged current processes ep → νX (bottom) by W-bosons.
Figure 1b: Graphical displays of measured events in the experiments. In the H1 neutral current event (left) the electron scattered at large angles e' is well visible, whereas in the charged current event (right), the neutrino escapes undetected, and only the remnants of the broken up proton (the hadronic final state X) are measured.

Figure 2: Measured reaction rates (cross sections) for neutral (NC, blue) and charged (CC, red) current processes as a function of the scaling variable Q2, for both e+p and e-p scattering [3]. The overlaid curves are theoretical predictions, based on standard model calculations.


2 Inelastic Electron - Proton Scattering

When colliding high energetic electrons with protons through inelastic scattering, the proton breaks up in the reaction. The relevant processes are electroweak interactions, which are either neutral current (NC: ep → e'X) or charged current (CC: ep → νX) reactions. A neutral photon or Z-boson is exchanged in NC, whereas in CC a charged W± boson is exchanged producing a neutral, undetected neutrino, as illustrated in Figure 1 (full details on the formalism can be found e.g. in [2]).

Experimentally, the kinematics of the reactions are determined by measuring either the scattered lepton e' (NC case) or all the hadronic particles X emerging from the broken up proton (CC case). One of the most important Lorentz variables used for the description of the reaction kinematics is the squared momentum transfer of the exchanged boson (γ, Z, W), denoted by Q2 = -q2 = -(k - k')2, where k, k' are the four-momenta of the incoming and scattered electron. The attainable "spatial" resolution available to probe the composite proton can therefore be characterised by the scale Q = |q|, i.e. λ≈ (200MeV/|q|) fm, which at HERA reaches the level of 10-18 m.

In general terms, the cross sections for ep-scattering, which describe the reaction rates, are determined by the electroweak interactions using the couplings of the pointlike electrons, the properties of the exchanged bosons (γ, Z,W), and a set of inelastic structure functions Fi. These Fi are the quantities of interest here, as they are the functions that parametrise the composite structure of the proton and need to be determined by experiment.

Precise measurements of the ep-scattering rates determined by the H1 and ZEUS experiments are summarised in Figure 2 as a function of the scaling variable Q2, for both neutral and charged current interactions [3]. They illustrate some of the main features of these electroweak processes. In NC reactions (blue), photon exchange is the dominating process at small scales Q2, and Z-exchange becomes sizeable only at high Q2. In CC reactions (red) the heavy mass of the exchanged W-boson strongly suppresses the reaction rate already at low Q2. When in the high Q2 regime the masses of Z and W bosons (91.2 and 80.4 GeV) become less relevant in comparison with the reaction scales Q2, both the NC and CC rates become similar in size, illustrating the unification of electromagnetic and weak interactions.

Figure 3: Measured reaction rates (reduced cross sections) for neutral current processes, as a function of the scaling variable Q2 for different values of x, the proton momentum fraction carried by the partons. These results represent the combined analysis of H1 and ZEUS. Scaling violations, i.e. a Q2 - dependence of the rates, are clearly observed. The curves represent the description, based on the theory of strong interactions (see [4]).

3 The Proton Structure

In the so-called quark parton model (QPM), the proton is described as a composite object, made of valence quarks (two up and one down quark), sea quarks (pairs of up, down, strange, charm and bottom quark-antiquarks) and the gluons, which serve as the mediating carriers of the strong force binding the quarks within the proton. Within the QPM, ep-scattering is described by an incoherent sum of elastic scattering of the exchanged bosons (γ, Z, W) on these partons in the proton. Within this QPM framework, the abovementioned generic proton structure functions Fi are directly related to combinations of the so-called parton distribution functions xqi(x), referred to as ”PDFs”. These PDFs describe the probability that a certain parton i carries a fraction x of the total proton momentum, and thus characterise the proton structure at the parton level. Precise measurements of these Fi therefore allow a determination of the PDFs.

In the framework of the theory of strong interactions (QCD), the functions qi(x) depend also on the reaction scale, and this Q2 - dependence can be accurately described by evolution equations (see e.g. [2]). However, the x-dependencies of the PDFs can only be determined from the experimental data, using elaborated fitting procedures, as performed by various groups. Herein, the individual PDFs as extracted by the HERA working group based on HERA data only are discussed. Measurements from a variety of other experiments, such as from fixed target, proton-antiproton scattering or from neutrino experiments can also contribute information on the PDFs.

The combined H1 and ZEUS measurements of the reaction rates are shown in Figure 3 as a function of the scaling variable Q2 for different x values. They are presented here in form of so-called reduced cross sections σγ, which are directly proportional to the dominant structure function F2 associated to pure photon exchange. Using the QPM picture, these data provide direct sensitivity to the valence quark content of the proton at high x, and to sea quarks and gluons at low x values. Demonstrating the explicit Q2 -dependence of the NC processes in Figure 3 not only confirms “scaling violations”, but also illustrates the level of precision reached by the HERA experiments, spanning over four orders of magnitude in (x,Q2), seamlessly extending the previous fixed target regime (indicated by the squares). It is a remarkable achievement of the theory of strong interactions (QCD), that the calculations (red curves) are able to describe all the data so accurately over this huge kinematic range.

These precise data allowed the "HERA structure function working group" to extract the individual parton distribution functions xqi(x) for the various partons of the proton [4], as shown in Figure 4. Prominently visible are the valence quark contributions (the down quark xdv and the twice as frequent up quarks xuv), peaking around x ≈ 1/3. This corresponds to the naive expectations, in which the total proton momentum is equally shared among the three valence quarks. However, when considering lower values of x, i.e. smaller momentum fractions, the sea quarks (xS) and the gluons (xg) (both downscaled by a factor of 20 for visibility in the figure) increase substantially and become completely dominant. This means, that at low x the proton appears to literally "boil with gluons"!

Finally, one can ask the obvious question "Are the quarks themselves again composite objects?" In analogy to the discovery of the proton charge radius in the 1950s, an extended quark charge would modify the standard model cross sections accordingly. The precise comparison of the Q2-dependence of the measured ep cross sections to the ones predicted by the standard theory revealed no deviations up to the largest Q2-values of ≈ 20000 GeV2 available at HERA (see [1] and also Figure 2). Thus, there is no indication of a quark substructure apparent down to a scale of order of 10-18 m.

In summary, even though not all data have been completely analysed yet, HERA has already allowed to push the knowledge about the parton momentum distributions in the proton to an unprecedented high precision. Among others, an unexpected substantial increase of gluons at low momentum fractions was observed. Overall, the theory describes the features of inelastic electron proton scattering very well in all details, which can be considered a great success of the theory of electroweak and strong interactions.

Figure 4: Parton distribution functions of the proton (PDFs labelled “HERAPDF0.2”) as obtained by the HERA Structure Functions Working Group [4], at a scale of Q2 = 10 GeV2. The PDFs (solid lines) are shown separately for the gluon (xg), the sea quarks (xS), (both scaled down for visibility by a factor of 20), and the valence quarks up xuv and down xdv. The uncertainties are indicated by the coloured bands.



[1] Details about the experiments and their numerous results can be found at www-h1.desy.de for the H1 and at zeus.desy.de for the ZEUS collaborations.
[2] “Deep inelastic scattering”, R. Devenish and A. Cooper-Sarkar, Oxford Univ. Press 2004.
[3] H1 and ZEUS Collaborations: Contributions to the Int. Conference QCD2009, March 2009, Moriond, France; see e.g. moriond.in2p3.fr/QCD/2009/Proceedings09/Placakyte.pdf.
[4] Technical details of the measurements can be found e.g. in Eur. Phys. J. C 30 (2003) 1, for H1; in Eur. Phys. J. C 49 (2007) 523, for ZEUS. The figures shown here are the latest results, presented at the Int. Conference DIS2009, April 2009, Madrid, Spain (see V. Radescu for HERA at www.ft.uam.es/DIS2009 ).



[Released: July 2009]